Movement system configured for moving a payload in a plurality of directions

ABSTRACT

A movement system includes a bridge crane, a trolley, and a movement device. The movement device includes an attachment portion, a plurality of housings, first and second curved elements, a cable, and a cable angle sensor. The curved elements are pivotally attached to housings and perpendicularly overlap with one another such that a first slot defined in the first curved element is perpendicular to a second slot defined in the second curved element. The first curved element is pivotable about a first axis and the second curved element is configured to pivot about a second axis. The cable extends from the attachment portion and through each of the slots. The cable is pivotable to angularly displace at least one of the curved elements about a respective axis. The cable angle sensor is configured to measure the angular displacement of the at least one of the first and second curved elements.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 61/555,859 filed on Nov. 4, 2011, which is herebyincorporated by reference in its entirety.

TECHNICAL FIELD

The present disclosure relates to a movement system that is configuredfor moving a mass in a plurality of directions.

BACKGROUND

Overhead bridge cranes are widely used to lift and relocate largepayloads. Generally, the displacement in a pick and place operationinvolves three translational degrees of freedom and a rotational degreeof freedom along a vertical axis. This set of motions, referred to as aSelective Compliance Assembly Robot Arm (“SCARA”) motions or“Schönflies” motions, is widely used in industry. A bridge crane allowsmotions along two horizontal axes. With appropriate joints, it ispossible to add a vertical axis of translation and a vertical axis ofrotation. A first motion along a horizontal axis is obtained by moving abridge on fixed rails while the motion along the second horizontal axisis obtained by moving a trolley along the bridge, perpendicularly to thedirection of the fixed rails. The translation along the vertical axis isobtained using a vertical sliding joint or by the use of a belt. Therotation along the vertical axis is obtained using a rotational pivotwith a vertical axis.

There are partially motorized versions of overhead bridge cranes thatare displaced manually along horizontal axes and rotated manually alongthe vertical axis by a human operator, but that include a motorizedhoist in order to cope with gravity along the vertical direction. Also,some bridge cranes are displaced manually along all of the axes, but theweight of the payload is compensated for by a balancing device in orderto ease the task of the operator. Such bridge cranes are sometimesreferred to as assist devices. Balancing is often achieved bypressurized air systems. These systems need compressed air in order tomaintain pressure or vacuum—depending on the principle used—whichrequires significant power. Also, because of the friction in thecompressed air cylinders, the displacement is not very smooth and caneven be bouncy. Balancing can be achieved using counterweights, whichadd significant inertia to the system. Although helpful and evennecessary for the vertical motion, such systems attached to the trolleyof a bridge crane add significant inertia regarding horizontal motiondue to moving the mass of these systems. In the case of balancingsystems based on counterweights, the mass added can be very large, evenlarger than the payload itself. If the horizontal traveling speed issignificant, the inertia added to the system becomes a major drawback.

There are also fully motorized versions of such bridge cranes thatrequire powerful actuators, especially for the vertical axis of motionwhich has to support the weight of the payload. These actuators aregenerally attached to the trolley or bridge and are then in motion. Thevertical translation actuator is sometimes attached to the bridge andlinked to the trolley by a system similar to what is used in towercranes.

SUMMARY

A movement system is configured for moving a payload. The movementsystem includes a bridge crane, a trolley, and a movement device. Thebridge crane is configured for movement along an X axis. The trolley ismovably attached to the bridge crane and configured for movement along aY axis, in perpendicular relationship to the X axis. The movement devicedepends from the trolley. The movement device includes an attachmentportion, a plurality of housings, a first curved element, a secondcurved element, a cable, and a cable angle sensor. The housings eachoperatively extend from the attachment portion. The first curved elementand the second curved element extend between respective ends. The endsof the first and second curved elements are pivotally attached to arespective one of the plurality of housings. Each of the first andsecond curved elements form a partial circle. The first curved elementdefines a first slot and the second curved element defines a secondslot. The first curved element perpendicularly overlaps with the secondcurved element such that the first slot of the first curved element isin perpendicular relationship to the second slot of the second curvedelement. The first curved element is configured to pivot about a firstaxis and the second curved element is configured to pivot about a secondaxis, which extends in perpendicular relationship to the first axis. Thecable extends from the attachment portion and through each of the firstslot and the second slot. The cable is configured to pivot relative tothe attachment portion such that the cable angularly displaces at leastone of the first and second curved elements about the respective firstand second axis. The cable angle sensor is configured to measure theangular displacement of the at least one of the first and second curvedelements.

A movement device is configured to determine a direction of intendedmovement of a payload. The movement device includes an attachmentportion, a plurality of housings, a first curved element, a secondcurved element, a cable, and a cable angle sensor. Each of the housingsoperatively extend from the attachment portion. The first and secondcurved elements each extend between respective ends. The ends of thefirst and second curved elements are pivotally attached to a respectiveone of the plurality of housings. Each of the first and second curvedelements form a partial circle. The first curved element defines a firstslot and the second curved element defines a second slot. The firstcurved element perpendicularly overlaps with the second curved elementsuch that the first slot of the first curved element is in perpendicularrelationship to the second slot of the second curved element. The firstcurved element is configured to pivot about a first axis and the secondcurved element is configured to pivot about a second axis, which extendsin perpendicular relationship to the first axis. The cable extends fromthe attachment portion and through each of the first and second slots.The cable is configured to pivot relative to the attachment portion suchthat the cable angularly displaces at least one of the first and secondcurved elements about the respective first and second axis. The cableangle sensor is configured to measure the angular displacement of the atleast one of the first and second curved elements.

A method of moving a movement device along at least one of an X axis anda Y axis includes providing a cable angle sensor configured to measureangular displacement of at least one of a first and a second curvedelement about a respective first and second axis. A cable is disposedvertically through each of a first and a second slot defined in therespective first and second curved element. An angle is imparted to thecable such that the cable causes an angular displacement of at least oneof the first and second curved elements about the respective first andsecond axis. The angular displacement of the at least one of the firstand second curved elements about the respective first and second axis isdetermined. The movement device is moved along the at least one of the Xaxis and the Y axis in response to the determination of the angulardisplacement of the at least one of the first and second curved elementsabout the respective first and second axis until the cable is vertical.

The above features and advantages, and other features and advantages ofthe present disclosure, will be readily apparent from the followingdetailed description of the embodiment(s) and best mode(s) for carryingout the described invention when taken in connection with theaccompanying drawings and appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic perspective view of a movement system including amovement device which is connected to a support structure and configuredfor moving a payload attached to a cable;

FIG. 2 is a schematic perspective view of cable angle sensor configuredfor measuring an angular displacement of the cable;

FIG. 3 is an exploded schematic perspective view of a housing, sensors,and a shaft of the cable angle sensor of FIG. 2;

FIG. 4 is a schematic perspective view of the movement device supportingthe payload;

FIGS. 5A-5C are schematic diagrammatic views of parameter definitions ofthe movement system;

FIG. 6 is a schematic block diagram of a high frequency oscillationscheme usable with the controller shown in FIG. 1;

FIG. 7 is a schematic block diagram of a control scheme usable with thecontroller shown in FIG. 1;

FIG. 8 is a schematic block diagram of an acceleration estimation with afusion method;

FIG. 9 is a schematic block diagram of a float mode control scheme; and

FIG. 10 is another schematic block diagram of a control scheme of thefloat mode.

DETAILED DESCRIPTION

Referring to the drawings, wherein like reference numbers refer to likecomponents, a movement system 10 configured for moving a payload 12 in aplurality of directions is shown at 10 in FIG. 1. The movement system 10is mounted to a stationary support structure 14 that is configured tosupport the movement system 10 and the payload 12. The support structure14 includes, but is not limited to a pair of parallel rails 16 or runwaytracks.

Referring to FIG. 1, the movement system 10 includes a bridge crane 18,a trolley 20, and a movement device 22. The bridge crane 18 is astructure that includes at least one girder 30 that spans the pair ofparallel rails 16. The bridge crane 18 is adapted to carry the payload12 along an Y axis 17. The trolley 20 is movably attached to girders 30of the bridge crane 18 such that the trolley 20 is adapted to carry thepayload 12 along an X axis 19, in generally perpendicular relationshipto the Y axis 17. The movement device 22 is operatively attached to thetrolley 20. A Z axis 21 extends in a vertical direction, with respect tothe ground G, and is defined between the intersection of the X axis 19and the Y axis 17.

Referring to FIGS. 1 and 2, the movement device 22 includes a cableangle sensor 24, a suspended cable 26, a cart 28, and a controller 32.The cable 26 is configured for supporting the payload 12. The cableangle sensor 24 is configured to measure two degrees-of-freedom of thecable 26. Additionally, the movement device 22 is configured to allowthe operator 33 to place their hands 35 anywhere directly on the payload12. By being in close contact with the payload 12, it is easier for theoperator to manipulate and to guide the movement device 22. When theoperator is not restricted as to where to place their hands 35, theoperator's 33 hand 35 placement can be adjusted to be more efficient,productive, comfortable, and to provide the operator with a clearer viewof the task at hand. Direct placement of the operator's 33 hands 35 onthe payload 12 may also allow the operator to maneuver the payload 12with only one hand 35, while using the other hand 35 for another aspectof the task. Additionally, direct access to the payload 12 may allowmany operators 33 to contact the payload 12 at the same time, since thesystem is configured to measure the result of the operators 33 combinedapplied forces to the payload 12.

Referring to FIGS. 1 and 5, during operation, the operator 33 imparts anangle θ₁ and θ₂ to the cable 26, by pushing or otherwise applying aforce F to the payload 12 in an X-Y plane. These angles θ₁ and θ₂ aremeasured by the cable angle sensor 24. The controller 32 is operativelyconnected to the movement device 22. The controller 32 is configured tomove the cart 28 along the X axis 19 and/or the Y axis 17 in order tokeep the cable 26 vertical (along the Z axis 21). Thus, the cart 28moves in the direction desired by the operator 33 (direction of cable 26displacement), while controlling the cable 26 sway, resulting inassistance to the operator 33 in moving the payload 12 along the X axis19 and the Y axis 17. Since the controller 32 ensures that the cable 26remains vertical, the operator 33 is not required to stop the payload 12manually, since the controller 32 manages to cause the payload 12 tostop. Additionally, an autonomous mode, where the payload 12 position isprescribed, while reducing cable 26 sway may also be provided.

The cable angle sensor 24 may be configured to be absolute, precise, lowcost, and provide high resolution in order to achieve the controlobjectives. The controller 32 is based on simplified cable 26 dynamicswith state space control to provide cooperative motion and autonomousmotion. The controller 32 may be modified to vary parameters, such asthe cable 26 length. Additionally, the controller 32 does not need amass of the cart 28 or the payload 12, but rather, adapts to varyingparameters while being robust and intuitive to the operator 33.

Referring again to FIG. 2, the cable angle sensor 24 includes a firstcurved element 36 and a second curved element 38. Each curved elementextends between respective ends 40. The curved elements 36, 38 each forma partial circle and are concentric such that they share a commoncenter. The first element 36 defines a first slot 44 and the secondelement 38 defines a second slot 46. Each slot extends longitudinallybetween the respective ends 40. The first curved element 36perpendicularly overlaps the second curved element 38 such that the slotof the first curved element 36 is in perpendicular relationship to theslot of the second curved element 38. The ends 40 of the curved elements36, 38 are pivotally attached to a respective housing 48. The housings48 are operatively attached to a mounting plate 50 (FIG. 4) such thatthe first curved element 36 pivots about a first axis 52 and the secondcurved element 38 pivots about a second axis 54, which extends inperpendicular, intersecting relationship to the first axis 52. A shaft56 pivotally interconnects each of the ends 40 and the respectivehousing 48. More specifically, referring to FIG. 3, the shafts 56 aresupported in the respective housing 48 by two bearings 58, ensuring thatthe rotation of the shaft 56 about the respective first and second axis52, 54 is straight and the friction is low.

Referring to FIG. 4, the cable 26 passes through the first slot 44 andthe second slot 46. A pivot point 60 of the cable 26 should be alignedwith each of the slots 44, 46 such that the cable 26 passes straightthrough the curved elements 36, 38 to prevent biased readings that mightotherwise result due to the cable 26 bending around the curved elements36, 38. Additionally, a portion of the slot 44 of the first curvedelement 36 overlaps with a portion of the slot 46 of the second curvedelement 38, throughout the angular displacement θ₁ and θ₂ of the firstand second curved elements 36, 38, caused by the movement of the cable26, which passes through the slots 44, 46. A guide 85 may be used tomake sure the cable pivot point 60 stays the same. The slots 44, 46 maybe configured to be slightly larger than the diameter of the cable 26.Flexible elements may be disposed in the slots 44, 46 to close the gap.The flexible elements may help prevent backlash from the cable 26interfering with the slot, while maintaining easy movement of the cable26 within the slots 44, 46.

Because there are two shafts 56 for each of the first axis 52 and thesecond axis 54, and each shaft 56 has two sides 62, several sensors 64may be used for each axis. By way of a non-limiting example, an encoder66 and a Hall effect sensor 68 may be used for each of the first axis 52and the second axis 54. Although only one sensor per axis may besufficient, combining the encoder 66 with the Hall effect sensor 68provides many benefits. First of all, the signals from the encoder 66and the Hall effect sensor 68 may be combined using data fusion toobtain a signal of better quality. Second of all, it is possible tocompare both signals to detect problems, i.e., inaccuracies in theindividual signals. Finally, the absolute signal of the Hall effectsensor 68 may be used, while taking advantage of the encoder 66precision. Other sensors 64 could also be used. Absolute encoders 66,potentiometers or linear accelerometers (used as inclinometers) could beused as position sensor. A gyroscope could be used to obtain the angularvelocity while an accelerometer could be used to obtain angularacceleration. Accelerometers or gyroscopes placed on the slotted partscould also help determine different dynamical effects. Photointerruptorscould also be used at strategic places. Finally, the above signal can bederived/integrated to obtain corresponding signals.

The cart 28 is configured for moving the bridge crane 18 and/or thetrolley 20 along the respective X axis 19 and Y axis 17 in response tothe application of the force F to the payload 12. As the force F isapplied to the payload 12 a direction along the X axis 19 and/or the Yaxis 17, movement of the cable 26 within the slots 44, 46 of the curvedelements 36, 38 causes the curved elements 36, 38 to rotate an angle θ₁,θ₂ about the respective first and second axes 52, 54. The sensors 64measure an angle of rotation θ₁, θ₂ of the curved elements 36, 38 aboutthe respective first and second axes 52, 54.

In order to be desensitized to small angle measurement precision errors,a deadband on the angle may be used. The deadband is an area of a signrange where no action on the system occurs. The movement device 22 mayalso be excited by small amplitude, high frequency unmodeled dynamics orit may be difficult for the control to manage high frequencyoscillations. During oscillations, when the cable 26 is close to avertical position, since the angle measurement often changes sign, itbecomes difficult to suppress the oscillations. An algorithm, shown asan oscillation logic block 70, is provided to compensate for highfrequency oscillations, while keeping precision and performance to keepthe cable 26 vertical. It should be appreciated that one of the signalsmay be, for example, θ₁. For a small deadband, θ_(db1) is used to copewith precision errors of the angle measurements. Two other angles aredefined, θ_(db2) and θ_(db3). The signal θ_(p0) is determined in adeadband block 72 and expressed as follows:

$\theta_{p\; 0} = \{ \begin{matrix}0 & {{{if} - \theta_{{db}\; 1}} < \theta < \theta_{{db}\; 1}} \\{\theta - \theta_{{db}\; 1}} & {{{if}\mspace{14mu} \theta} > \theta_{{db}\; 1}} \\{\theta + \theta_{{db}\; 1}} & {{{if}\mspace{14mu} \theta} < {- \theta_{{db}\; 1}}}\end{matrix} $

and the signal θ_(p1) is determined in a deadband and saturation block74 and expressed as follows:

$\theta_{p\; 1} = \{ \begin{matrix}0 & {{{if} - \theta_{{db}\; 2}} < \theta < \theta_{{db}\; 2}} \\{\theta - \theta_{{db}\; 2}} & {{{if}\mspace{14mu} \theta_{{db}\; 2}} < \theta < \theta_{{db}\; 3}} \\{\theta + \theta_{{db}\; 2}} & {{{if} - \theta_{{db}\; 2}} > \theta > {- \theta_{{db}\; 3}}} \\{\theta_{{db}\; 3} - \theta_{{db}\; 2}} & {{{if}\mspace{14mu} \theta} > \theta_{{db}\; 3}} \\{{- \theta_{{db}\; 3}} + \theta_{{db}\; 2}} & {{{if}\mspace{14mu} \theta} < {- \theta_{{db}\; 3}}}\end{matrix} $

The signal θ_(p0) then corresponds to the input angle signal aboveθ_(db1) while θ_(p1) corresponds to the input signal between θ_(db2) andθ_(db3). In order to remove the high frequency oscillations from θ_(p1),this signal is further processed. Because the natural and desired cable26 position is vertical, a filtering algorithm may be used, as shown at70 in FIG. 6. The absolute signal of θ_(p1) is determined in an absolutelogic block 76 and then the absolute signal passes through a ratelimiter block 78. The rising limit is low and the falling limit is high,such that it takes time for the output signal to increase, filteringhigh frequency oscillations. However, the signal of the θ_(p1) canreturn to zero rapidly, avoiding a phase shift. This signal is thenmultiplied by the sign of θ_(p1), stored in a sign block 82. Theresulting signal, can then optionally be slightly filtered with a usuallow pass filter at a low pass block 80, resulting in the signal θ_(p2).Although, θ_(p0) and θ_(p2) can be used individually in the control,they can also be grouped as:

θ_(pf)=θ_(p0)+θ_(p2)

Referring to FIGS. 5A-5C, a relation between the angles β_(i) and θ_(i)needs to be obtained. A unit vector e, is aligned with the cable 26 andthe cable's 26 endpoint coordinates are [X_(S), Y_(S), Z_(S)]^(T). Thecross product between e and unit vector [0 1 0] gives the normal to theplan σ₁ in which the cable 26 lies. The dot product of these resultswith the unit vector [1 0 0] leads to the angle θ₁ cosine. The angle θ₂cosine is obtained similarly. Also, using the fact that X²+Y²+Z²=1:

${{{dynamical}\mspace{14mu} \cos \mspace{14mu} \theta_{1}} = \frac{\sqrt{1 - X_{s}^{2} - Y_{s}^{2}}}{\sqrt{1 - Y_{s}^{2}}}},{{\cos \; \theta_{2}} = \frac{\sqrt{1 - X_{s}^{2} - Y_{s}^{2}}}{\sqrt{1 - X_{s}^{2}}}}$

The unit vector e coordinates are:

X_(S)=sin θ₁ cos β₁

Y_(S)=sin β₁

Z_(S)=cos θ₁ cos β₁

The correspondence is:

${\cos \; \beta_{1}} = \frac{\cos \; \theta_{2}}{\sqrt{1 - {\sin^{2}\theta_{1}\sin^{2}\theta_{2}}}}$${\sin \; \beta_{1}} = \frac{\cos \; \theta_{1}\sin \; \theta_{2}}{\sqrt{1 - {\sin^{2}\theta_{1}\sin^{2}\theta_{2}}}}$

Taking the derivatives of any questions of the previous equation leadsto:

${\overset{.}{\beta}}_{1} = \frac{{{\overset{.}{\theta}}_{2}\cos \; \theta_{1}} - {{\overset{.}{\theta}}_{1}\sin \; \theta_{1}\cos \; \theta_{2}\sin \; \theta_{2}}}{1 - {\sin^{2}\theta_{1}\sin^{2}\theta_{2}}}$

In the following, the equations of motion are first obtained with acomplete model called coupled motion. Then, with simplifications, asimplified model is obtained. With reference to FIGS. 1-4 and theparameters defined in FIGS. 5A-5C, the measured variable from the cableangle sensors 24 are θ₁, corresponding the first axis 52, and θ₂,corresponding to the second axis 54. The equations of motion for thepayload 12 position are:

X _(p) =X _(C) +L _(p) sin θ₁ cos β₁

Y _(p) =Y _(C) +L _(p) sin β₁

Z _(p) =L _(p) cos θ₁ cos β₁

where X_(p), Y_(p) and Z_(p) are the payload 12 center of mass 42position in fixed coordinates, X_(C) and Y_(C) are the cart 28coordinates in fixed coordinates, and L_(p) is the distance between thecable pivot point 60 and the payload 12 center of mass 42. The potentialenergy is provided as follows:

V =−mgL _(p) cos β₁ cos θ₁

where m is the payload 12 mass and the kinetic energy is expressed as:

$T = {{\frac{1}{2}M_{x}{\overset{.}{X}}_{c}^{2}} + {\frac{1}{2}M_{y}{\overset{.}{X}}_{c}^{2}} + {\frac{1}{2}{m( {{\overset{.}{X}}_{p}^{2} + {\overset{.}{Y}}_{p}^{2} + {\overset{.}{Z}}_{p}^{2}} }}}$

where M_(X) is the cart 28 mass in the X direction and M_(Y) is the cart28 mass in the Y direction. One should note that the cable 26 mass wasneglected. The equations of motion are obtained from the previous twoequations and the Lagrange method as follows:

F _(X) =M _(x) {umlaut over (X)} _(C) +m({umlaut over (X)} _(C) +{umlautover (L)} _(p) cos β₁ sin θ₁ −L _(p) sin β₁ sin θ₁ {umlaut over (β)}₁ −L_(p) cos β₁ sin θ₁{dot over (β)}₁ ² −L _(p) cos β₁ sin θ₁{dot over(θ)}²+2 cos β₁ cos θ₁ {dot over (L)} _(p){dot over (θ)}₁−2L _(p) sin β₁cos θ₁ {dot over (β)}₁{dot over (θ)}₁−2{dot over (L)} _(p){dot over(β)}₁ sin β₁ sin θ₁ +L _(p) cos θ₁ cos β₁ {umlaut over (θ)}₁)

F _(Y) =M _(y) Ÿ _(c) +m(Ÿ _(c)+2{dot over (L)} _(p){dot over (β)}₁ cosβ₁ −L _(p){dot over (β)}₁ ² sin β₁ +L _(p) cos β₁ {umlaut over (β)}₁+{umlaut over (L)} _(p) sin β₁)

F _(L) =m({umlaut over (X)} _(c) cos β₁ sin θ₁ +{umlaut over (L)} _(p)+Ÿ _(c) sin β₁ −L _(p){dot over (β)}₁ ² −L _(p){dot over (θ)}₁ ² cos² β₁−g cos β₁ cos θ₁)

F _(Z)=0=M _(z) {umlaut over (Z)} _(c) +m({umlaut over (Z)} _(c) +L cosθ₁ {dot over (θ)}₁ ² +L sin θ₁{umlaut over (θ)}₁ +L cos θ₂ {dot over(θ)}₂ ² +L sin θ₂{umlaut over (θ)}₂ +g)

F _(θ1)=0=m(L{umlaut over (θ)} ₁ +{umlaut over (x)} cos θ₁ +g sinθ₁+2{dot over (L)} _(p){dot over (θ)}₁ cos β₁−2L _(p){dot over (θ)}₁{dotover (β)}₁ sin β₁)L cos β₁

F _(β1)=0=m(L _(p){umlaut over (β)}₁ +L _(p) ÿ cos β₁ −{umlaut over (x)}sin β sin θ+2{dot over (β)}₁ {dot over (L)}+L _(p){dot over (θ)}₁ ² cosβ₁ sin β₁ +mg sin β₁ cos θ₁)L _(p)

One should note that similar equations could be found with the otherangle representation as (θ₂, β₂). Additionally, the coupling betweenangles θ₁ and θ₂ is negligible for relatively small angles and angularvelocities. Thus, motion along the X axis 19 and Y axis 17 will betreated separately, as described below.

With only one degree-of-freedom and a small rotation rate, where θrefers to θ₁ or θ₂, while the other angle remains fixed, equations ofmotion are as follows:

F=(M+m){umlaut over (x)}+m{umlaut over (θ)}L cos θ−mL{dot over (θ)} ²sin θ+m{umlaut over (L)} sin θ+2m{dot over (θ)}{dot over (L)} cos θ

τ=0=({umlaut over (x)} cos θ+g sin θ+L{umlaut over (θ)}+2{dot over(L)}{dot over (θ)})mL

which can be simplified to the pendulum equations for constant cable 26length L as follows:

F=(M+m){umlaut over (x)}+m{umlaut over (θ)}L cos θ−mL{dot over (θ)} ²sin θ

τ=0=({umlaut over (x)} cos θ+g sin θ+L{umlaut over (θ)})mL

where M is the mass of the cart 28 and m is the mass of the payload 12.Assuming small angles and a slowly varying vertical translation andneglecting {dot over (θ)}², the equations can be linearized as follows:

F=(M+m){umlaut over (x)}+m{umlaut over (θ)}L

0={umlaut over (x)}+gθ+L{umlaut over (θ)}

where L is considered constant over a time step and also corresponds toL_(p).

The movement mechanism may be operated in a cooperation mode allowingthe operator 33 to operate the movement device 22 by placing their hands35 directly on the payload 12. The movement mechanism allows theoperator 33 to impart an angle to the cable 26 by pushing the payload12, and this angle is measured by the sensors 64 as a rotation (θ₁ andθ₂) of the first and second curved elements 36, 38 about the respectivefirst and second axes 52, 54. The control system moves the cart 28 inresponse to the angle θ₁ and θ₂ of the cable 26 measured by the sensors64 to keep the cable 26 vertical. Thus, the cart 28 moves in thedirection desired by the operator 33, while controlling any sway of thecable 26, resulting in assistance to the operator 33 in moving thepayload 12 in the X and Y directions. Additionally, since the controller32 ensures that the cable 26 remains vertical, the operator 33 is notrequired to manually stop the load, since the control system managesitself to stop the payload 12. An autonomous mode, where the payload 12position is prescribed, while reducing cable 26 sway, may also bedesired.

The force F required for an operator 33 to move the payload 12 would bereduced because a measure of the imparted angle(s) θ₁ and θ₂ of thefirst and second curved elements 36, 38 about the respective first andsecond axes 52, 54 can be precisely and accurately measured. Thisresults in a system that moves along the corresponding X axis 19 and/orY axis 17.

The controller 32 includes a control block 86, shown in FIG. 7, which isconfigured to operate for cooperative motion or autonomous motion. Usingonly the last equation above, the cart 28 acceleration is considered asthe input. The payload 12 and cart 28 mass do not need to be known. Thefollowing equations are therefore obtained in a Laplace domain asfollows:

{umlaut over (X)}(s)+gθ(s)+s ² Lθ(s)=0

The state-space representation is as follows:

{dot over (x)} _(s) =A _(s) x _(s) +B _(s) u _(s)

y _(s) =C _(s) x _(s) +D _(s) u _(s)

where y_(S) the output vector, x _(S) is the state vector, u_(s) is theinput scalar, A_(S) is an n×n state matrix, B_(S) is an n×m inputmatrix, C_(S) is a p×n output matrix, D_(S) is a p×m feed through matrixand where n is the number of states, m is the number of inputs and p isthe number of outputs. Here, x _(S)=[x {dot over (x)} θ {dot over(θ)}]^(T) and u_(S)={umlaut over (x)}, with

$A_{s} = {{\begin{bmatrix}0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 0 & \frac{- g}{L} & 0\end{bmatrix}\mspace{14mu} {and}\mspace{14mu} B_{s}} = \begin{bmatrix}0 \\1 \\0 \\\frac{- 1}{L}\end{bmatrix}}$

The above equation, obtained from the Laplace domain, is used, whereu={umlaut over (x)}, the control law is u_(S)=K_(R)e, where:

${K_{R} = {{\lfloor \begin{matrix}K_{x} & K_{v} & {- K_{\theta}} & {- K_{\theta \; p}}\end{matrix} \rfloor \mspace{14mu} {and}\mspace{14mu} e} = \begin{bmatrix}{x_{d} - x} \\{{\overset{.}{x}}_{d} - \overset{.}{x}} \\{\theta_{d} - \theta} \\{{\overset{.}{\theta}}_{d} - \overset{.}{\theta}}\end{bmatrix}}},$

where {dot over (x)}_(d), θ_(d), and {dot over (θ)}_(d) equal zero.

Referring again to the control logic block of FIG. 7, the input, u_(S),is the acceleration of the cart 28, and because controlling accelerationis not practical, velocity control is used in the cooperation mode andposition control is used in the autonomous mode. The output of thelatter lower level controller block 88 is shown as u₂ in FIG. 7.

In the cooperation mode, the state space controller block 90 output ofFIG. 7 is obtained as a discrete velocity with a zero-order-holdintegration, as follows:

{umlaut over (x)} _(d(k)) =u=K _(r) e

{dot over (x)} _(d(k)) ={dot over (x)} _(d(k-1)) +{umlaut over (x)}_(d(k)) T _(S)

Likewise, in the autonomous mode, the state space controller block 90output of FIG. 7 is obtained as a position by integrating once more, asfollows:

x _(d(k)) =x _(d(k-1)) +{dot over (x)} _(d(k-1)) T _(S)+0.5{umlaut over(x)} _(d(k)) T _(S) ²

One should note that the measured velocity could be used in thepreceding equations instead of the last time step desired value. Thisintegration method is used to achieve acceleration control in anadmittance control scheme. The desired acceleration is then obtained byusing velocity or position control, which is more practical. It is alsopossible to additionally use computed torque control using the previousforce equations. Although the payload 12 and cart 28 mass would then berequired, an approximation is sufficient since feedback control is alsoused. Additionally, the payload 12 and cart 28 mass are not required inorder to adapt the state space controller block 90 gains to varyingparameters. Additionally, a limit and saturation block 92 may be usedfor virtual walls and to limit velocity and acceleration of the cart 28.

In the cooperation mode, since there is no reference position, K_(x) isset to zero. The control gain K_(θp), i.e., gain on the angular velocitysignal, can be optionally used, depending on the angle derivative signalquality. An adaptive controller 32, based on pole placement and statespace control may be used. The pole of the system may be obtained by:

det[s1−A+BK_(r)]

leading to the equation:

$\frac{{s^{3}L} + {s^{2}( {{K_{\theta}p} + {K_{v}L}} )} + {s( {g + K_{\theta}} )} + {K_{v}g}}{L}$

where K_(θ) and K_(θp) are assumed negative.

The transfer function from angle θ to an angle initial condition θ₀ isas follows:

$\frac{{\theta_{0}( {s + K_{v}} )}L_{s}}{{s^{3}L} + {s^{2}( {{K_{\theta}p} + {K_{v}L}} )} + {s( {g + K_{\theta}} )} + {K_{v}g}}$

The poles may be placed to the following:

(s+p₁)(s²+2ζ₁w_(n1)+w_(n1) ²)

In a first method, K_(v) and K_(θ) are used, which leads to thefollowing:

K_(v) = p₁ + 2ζ₁ω_(n 1)${\frac{g}{L} + \frac{K_{\theta}}{L}} = {\omega_{n\; 1}^{2} + {2\zeta_{1}\omega_{n\; 1}p_{1}}}$$\frac{K_{v}g}{L} = {p_{1}\omega_{n\; 1}^{2}}$

and then, the following are used:

$p_{1} = \frac{2g\; \zeta_{1}\omega_{n\; 1}}{{- g} + {\omega_{n\; 1}^{2}L}}$$K_{v} = \frac{p_{1}\omega_{n\; 1}^{2}L}{g}$$K_{\theta} = {( {\omega_{n\; 1}^{2} - \frac{g}{L} + {2\zeta \; \omega_{n\; 1}p_{1}}} )L}$${{where}\mspace{14mu} \omega_{n\; 1}} \geq \sqrt{\frac{g}{L}}$

and ζ are design parameters. The control gains are thus obtained. Thetransfer function zero influences the response, but without practicaleffect, since it is relatively high, w_(n1) is chosen very close to

$\sqrt{\frac{g}{L}},$

but not too close to avoid numerical problems.

The control scheme is then used with these gains to manage thecooperation with the operator 33, while stabilizing the cable 26.

In a second method, K_(v), K_(θ), and K_(θp) are used, which leads tothe following:

${K_{v} + \frac{K_{\theta \; p}}{L}} = {p_{1} + {2\zeta_{1}\omega_{n\; 1}}}$${\frac{g}{L} + \frac{K_{\theta}}{L}} = {\omega_{n\; 1}^{2} + {2\zeta_{1}\omega_{n\; 1}p_{1}}}$$\; {\frac{K_{v}g}{L} = {p_{1}\omega_{n\; 1}^{2}}}$

The second method allows the poles to remain constant. Using the gainK_(θp) allows the cart 28 to move in regards to the angles θ₁ and θ₂ andangular velocity. The following is then obtained:

$p_{1} = \frac{- {g( {K_{\theta \; p} - {2{\zeta\omega}_{n\; 1}L}} )}}{L( {{- g} + {\omega_{n\; 1}^{2}L}} )}$$K_{v} = \frac{p_{1}\omega_{n\; 1}^{2}L}{g}$$K_{\theta} = {( {\omega_{n\; 1}^{2} - \frac{g}{L} + {2{\zeta\omega}_{n\; 1}p_{1}}} )L}$where ${\omega_{n\; 1} \geq \sqrt{\frac{g}{L}}},$

ζ, and K_(θp) are design parameters. The control gains are thusobtained.

The transfer function zero influences the response, but withoutpractical effect since it is relatively high, w_(n1) is chosen veryclose to

$\sqrt{\frac{g}{L}},$

but not too close to avoid numerical problems.

The control scheme is then used with these gains to manage thecooperation with the operator 33, while stabilizing the movement device22.

Neglected terms from the complete model as {dot over (L)}, {dot over(β)}, {dot over (θ)}² and viscous friction can be compensated for, forexample, with gains K_(θ) and K_(θp) by considering the terms constantover a time step, similarly as with the lengths L of the cable 26.

Control gains may also be heuristically modified from the computedgains. Additionally, control gains on θ_(p0) and θ_(p2) and theirderivatives may be different from each other.

In the autonomous mode, K_(x) is used to control the cart 28 position.The control gain K_(θp) can be optionally used. An adaptive controller32 based on pole placement and state space control using K_(θp) isprovided. Similar to the cooperation mode, the system poles are:

$\frac{{s^{4}L} + {s^{3}( {{K_{\theta}p} + {K_{v}L}} )} + {s^{2}( {g + K_{\theta} + {K_{x}L}} )} + {s( {K_{v}g} )} + {K_{x}g}}{L}$

where K_(θ) and K_(θp) are assumed to be negative.

There is a compromise between the cart 28 position trajectory and thecable 26 oscillation cancellation. In regards to the equations, this isdue to the transfer function zeros.

Pole placement is used using the characteristic equation:

(s+p₁)²(s²+2ζ₁w_(n1)+w_(n1) ²)

Equaling the previous equations for the system poles and pole placementprovides:

${{2\zeta_{1}\omega_{n\; 1}} + {2\; p_{1}}} = {K_{v} + \frac{K_{\theta \; p}}{L}}$${\omega_{n\; 1}^{2} + {4\zeta_{1}\omega_{n\; 1}p_{1}} + p_{1}^{2}} = {\frac{K_{\theta}}{L} + K_{x} + \frac{g}{L}}$${{2\omega_{n\; 1}^{2}p_{1}} + {2\zeta_{1}\omega_{n\; 1}p_{1}^{2}}} = \frac{K_{v}g}{L}$${\omega_{n\; 1}^{2}p_{1}^{2}} = \frac{K_{x}g}{L}$

and then the following are used:where

$\omega_{n\; 1} \geq \sqrt{\frac{g}{L}}$

and ζ are design parameters and p₁ is heuristically chosen to be equalto w_(n1) as to lie on the same circle as the other poles. It is adesign choice to use two complex poles and two equal real poles as otherchoices are possible. The state space controller gains to adapt are thusobtained. The transfer function zero influence the response but withoutpractical effect since it is relatively high. A value of w_(n1) ischosen very close to

$\sqrt{\frac{g}{L}},$

but not too close to avoid numerical problems.

$K_{x} = \frac{\omega_{n\; 1}^{2}p_{1}^{2}L}{g}$$K_{v} = \frac{2\omega_{n\; 1}p_{1}{L( {\omega_{n\; 1} + {\zeta_{1}p_{1}}} )}}{g}$$K_{\theta} = {( {\omega_{n\; 1}^{2} + {4\zeta_{1}\omega_{n\; 1}p_{1}} + p_{1}^{2} - K_{x} - \frac{g}{L}} )L}$K_(θ p) = (2ζ₁ω_(n 1) + 2 p₁ − K_(v))L

One should note that the operator 33 can still push the payload 12 inautonomous mode. The cart 28 position will move in the direction desiredby the operator 33, while be attracted to its reference position andcancelling oscillations of the movement device 22. Depending on thecontrol gains, it will be more or less easy to move the cart 28 awayfrom its reference position. Referring to FIG. 7, the control block 86will then be used with these gains to manage autonomous and cooperationwith the operator 33, while stabilizing the movement device 22.

Neglected terms from the complete model as {dot over (L)}, {dot over(β)}, {dot over (θ)}² and viscous friction can be compensated for, forexample, with gains K_(θ) and K_(θp) by considering the terms constantover a time step, similarly as with the cable 26 length L.

Control gains can also be heuristically modified from the computedgains. Additionally, control gains on θ^(p0) and θ_(p2) and theirderivatives can be different from one another.

When switching between the modes, i.e., cooperation mode, autonomousmode, stopping, and the like, rude acceleration and jerk profile may berequired. The most frequent abrupt profile happens when switching modeswhen the cable 26 angles θ₁ and θ₂ are non-zero. “Bumpless” transfer orsmooth transfer between modes may be achieved. In one embodiment, thelast control input is memorized or observed. In another embodiment, themeasured velocity is memorized when the mode switch happens. In thecooperation mode, the output bumpless velocity is as follows:

v _(DesBumpl) =a _(bt) v _(mem)+(1−a _(bt))v _(des)

The variable a_(bt) is reinitialized at 1 when a mode switch happens andis then multiplied by b_(bt) at each time step. At first v_(DesBumpl) isthen equal to the measured velocity (v_(mem)) and after some time,depending on parameter b_(bt), a_(bt) goes to 0 and v_(DesBumpl) tov_(des). The goal is to go from the present velocity as the mode switchmoment (v_(mem)) to the desired velocity (v_(des)) in a smooth filteredway. For the autonomous mode, the desired position is first reset to themeasured position and the desired bumpless velocity is integrated toobtain a new desired position respecting this velocity. Furthersmoothing may also be possible by considering the acceleration in themode switch.

In addition to the movement in the X direction and Y direction, thepayload 12 may also be moved in a vertical direction, i.e., in the Zdirection. In order to control the vertical movement of the cable 26, awinch 94, in combination with a load cell 96 (or force sensor), and anaccelerometer 97 may be used. The winch 94 may use a DC motor with apulley to roll the cable 26 and thus change the length L of the cable26. The accelerometer 97 may be placed in line with the cable 26, nearthe attachment point 84 of the payload 12.

In order for the operator 33 to be able to apply forces anywhere on thepayload 12, vertical cooperation must be obtained. More specifically,vertical cooperation is movement of the payload 12 in the verticaldirection. To achieve vertical cooperation, the load cell 96 is placedin line with the cable 26, before the payload 12. A signal of the loadcell 96 depends on the inertial effects of the load. This signal is:

$\mspace{79mu} \begin{matrix}{f_{1\; {cell}} = {f_{H} + {m( \begin{matrix}{{{\overset{¨}{X}}_{c}\cos \; \beta_{1}\sin \; \theta_{1}} +} \\{{\overset{¨}{L}}_{p} - {L_{p}{\overset{.}{\beta}}_{1}^{2}} - {L_{p}{\overset{.}{\theta}}_{1}^{2}\cos^{2}\beta_{1}} + {{\overset{¨}{Y}}_{c}\sin \; \beta_{1}} - {g\; \cos \; \beta_{1}\cos \text{?}}}\end{matrix} }}} \\{= {f_{H} + {ma}_{p}}}\end{matrix}$ ?indicates text missing or illegible when filed

where f_(H) is the operator 33 force and a_(p) is the payload 12acceleration:

a _(p)=({umlaut over (X)} _(c) cos β₁ sin θ₁ +{umlaut over (L)} _(p) −L_(p){dot over (β)}₁ ² −L _(p){dot over (θ)}₁ ² cos² β₁ +Ÿ _(c) sin β₁ −gcos β₁ cos θ₁)

In order to estimate the payload 12 mass or the operator 33 force, thedynamical effects must be compensated for in the control. Some methodscompensating for the dynamical effects may include the individualcompensation method, the fusion method, the accelerator method, and thelike.

The individual method is used to compute each term of the previousequation individually. The estimation is then:

â_(pi)=({umlaut over (X)} _(c) cos β₁ sin θ₁ +{umlaut over (L)} _(p) −L_(p){dot over (β)}₁ ² −L _(p){dot over (θ)}₁ ² cos² β₁ +Ÿ _(c) sin β₁ −gco β ₁ cos θ₁)

where â_(pi) is the payload acceleration estimation with the individualmethod.

From the previous equation, several measures are needed. The cable angleθ₁ and θ₂ (from which β₁ and β₂ are deduced), are obtained with thecable angle sensor, as explained previously. The cable angular velocity{dot over (θ)}₁ and {dot over (θ)}₂, (from which {dot over (β)}₁ and{dot over (β)}₂ are deduced), are obtained from the cable anglederivatives (done here with the Kalman filter). However, rate gyroscopescould also be placed on the cable angle sensor shafts. The cable lengthL_(c) is obtained with a position sensor on the winch 94 motor shaft(done here with a potentiometer and an incremental encoder, which arefused together). The cable length L_(c) is the length between the cablepivot point 60 and the payload attachment point 84. The payload 12position, L_(p), is obtained with:

L _(p) =L _(c)+δ_(cm)

where δ_(cm) is an approximation of the payload 12 center of mass fromthe payload 12 attachment point 84. The cable vertical acceleration,{umlaut over (L)}_(p), is obtained from a fusion from the desiredacceleration and the cable length L measure second derivative. One ofthese two signals could also be used directly. A rotationalaccelerometer or a gyroscope could also be placed on the winch 94 motorshaft. The gyroscope signal should be derived to obtain the angularacceleration. From this, the measure of the cable vertical accelerationcan be obtained. The cart acceleration, {umlaut over (X)}_(C) and Ÿ_(C),is obtained from a fusion from the desired acceleration and the cablelength L measure second derivative. One of these two signals could alsobe used directly. The cart acceleration may also be obtained by placinga rotational accelerometer or a gyroscope (derivative) on the motorshafts. Linear accelerometers could also be placed on the cart 28. Theacceleration â_(pi) is then obtained by inputting all of these measuresand estimations into the previous equation.

The cable vertical acceleration {umlaut over (L)}_(p) and the cartacceleration {umlaut over (X)}_(C) and Ÿ_(C) are obtained by fusing thedesired acceleration with the position measure second derivative. Usingthe desired acceleration alone may be inexact, while the positionmeasure second derivative is known to be very noisy. However, fusing thesignals can take advantage of both by using Kalman filtering.

A third order acceleration model is used:

$A = \begin{bmatrix}1 & T_{s} & {0.5\; T_{s}^{2}} \\0 & 1 & T_{s} \\0 & 0 & 1\end{bmatrix}$B=[0 0 0]^(T)

C=[1 0 0]^(T)

to find the state estimate {circumflex over (x)}_(i)(k):

{circumflex over (x)} _(i)(k)=[ê _(i)(k){dot over (ê)}_(i)(k){umlautover (ê)}_(i)(k)]^(T)

The acceleration estimation is then reconstructed with:

{circumflex over (q)} _(i) =q _(di) +ê _(i)

{dot over ({circumflex over (q)})} _(i) ={dot over (q)} _(di) +{dot over(ê)} _(i)

{umlaut over ({circumflex over (q)})} _(i) ={umlaut over (q)} _(di){umlaut over (ê)} _(i)

where {circumflex over (q)}_(i), {dot over ({circumflex over (q)})}_(i),and {umlaut over ({circumflex over (q)})}_(i) are respectively theposition, velocity, and acceleration final estimation.

This leads to a more precise estimation than if the Kalman filter wasapplied directly to the signal q_(i). More specifically, the errorsignal has less amplitude and bandwidth than the joint signal so that itis easier to obtain a signal of quality, while reducing filteringdrawbacks. By way of a non-limiting example, if the filter parametersare set to high filtering values, the estimation will be closed to thedesired movement instead of being close to zero with a filter directlyon the joint signal.

For the cart acceleration, the idea is similar, but is more complex.More specifically, in X and Y cooperation mode, the desired velocity andacceleration are known, but not the desired position. It is notdesirable to integrate the desired velocity to obtain the desiredposition since it would drift with time. The error is then defined as:

e _(i) ={dot over (q)} _(di) −{dot over (q)} _(i)

and filtered with a Kalman second order model velocity model. Thevariable q_(i) can be inputted directly or after being slightly filteredas with a third order Kalman filter acceleration model. Jointacceleration is then reconstructed as with the cable verticalacceleration.

The individual method has the advantage of having no drift, contrarilyto the accelerometer method, and the dynamical effect estimation can beaccurate, since it can be done at the payload center of mass position.

One should note that the individual and fusion method could be used notonly for a suspended cable but also for other mechanisms, such as anarticulated mechanism, and the like.

In the fusion method, the accelerometer and the individual method arefused to seize the advantages of each method, as shown at 100 in FIG.10. The acceleration at the accelerometer position, L_(a), is firstobtained independently by the accelerometer and by the individualmethod. The corresponding individual terms and the accelerometer arefused at this position depending on the confidence of each term. Withthe corrected individual terms obtained in output, the acceleration iscomputed at the payload center of mass. The fusion at the accelerometerposition is done here with linear data reconciliation with the equality:

E ₁ +E ₂ +E ₃ +E ₄ =E ₅

where

E₁={umlaut over (L)}_(a)

E ₂ =L _(a){dot over (β)}₁ ² −L _(a){dot over (θ)}₁ ² cos² β₁

E ₃ =g cos β₁ cos θ₁

E ₄ ={umlaut over (X)} _(c) cos η₁ sin θ₁ +Ÿ _(c) sin β₁

E₅=a_(acc)

where a_(acc) is an accelerometer signal and E₁ to E₄ are obtained withthe individual method (L_(a) is known from the cable length L and thedistance from the accelerometer and the cable end point).

Using the Lagrangian method, the criteria is:

$J = {\frac{( {{\hat{E}}_{1} - E_{1\; m}} )^{2}}{\sigma_{E\; 1}^{2}} + \frac{( {{\hat{E}}_{2} - E_{2\; m}} )^{2}}{\sigma_{E\; 2}^{2}} + \frac{( {{\hat{E}}_{3} - E_{3\; m}} )^{2}}{\sigma_{E\; 3}^{2}} + \frac{( {{\hat{E}}_{4} - E_{4\; m}} )^{2}}{\sigma_{E\; 4}^{2}} + \frac{( {{\hat{E}}_{5} - E_{5\; m}} )^{2}}{\sigma_{E\; 5}^{2}} + {\lambda^{T}( {{\hat{E}}_{1} + {\hat{E}}_{2} + {\hat{E}}_{3} + {\hat{E}}_{4} - {\hat{E}}_{5}} )}}$

where Ê₁ is a given effect final estimation, E_(im) is the given effectinput measure or initial estimation and σ_(Ei), are confidence terms.The solution is given by:

E _(out) =E _(in) −W ⁻¹ H ^(T)(HW ⁻¹ H ^(T))⁻¹ HE _(in)

where

E_(in)=[E_(1m) E_(2m) E_(3m) E_(4m) E_(5m)]^(T)

E_(out)=[Ê₁ Ê₂ Ê₃ Ê₄ Ê₅]^(T)

H=[1 1 1 1 −1]

$W = {{diag}( {\frac{1}{\sigma_{E\; 1}},\frac{1}{\sigma_{E\; 2}},{\frac{1}{\sigma_{E\; 3}}.\frac{1}{\sigma_{E\; 4}}.\frac{1}{\sigma_{E\; 5}}}} )}$

Then, with Ê₁ to Ê₄, the payload acceleration estimation is computed:

${\hat{a}}_{p\; f} = {{\hat{E}}_{1} + {{\hat{E}}_{21}\frac{L_{p}}{L_{a}}} + {\hat{E}}_{3} + {\hat{E}}_{4}}$

where â_(pf) is the payload acceleration estimation with the fusionmethod at 100 in FIG. 10.

Referring now to FIG. 8, a general scheme of the fusion method is shown.

It would also be possible to add other accelerometers (or fuse onlyaccelerometers) or other sensors and fuse them with the same techniqueby slightly modifying the above vectors or to use fusion with Kalmanfiltering, and the like. It should be appreciated that the individualmethod and the fusion method may also be used with other mechanisms,such as an articulated mechanism, and the like.

The mass of the payload 12 may also be monitored for reasons whichinclude, but are not limited to knowing if the device is loaded or ifthe mass exceeds the payload limit, and the like. This information couldalso be used in the position or velocity control to enhance theperformances. It may also be used to estimate the payload mass prior toentering a float mode 102. More specifically, the mass will be needed toestimate the applied human force, as will be explained in more detailbelow. If, for example, the estimate is {circumflex over(m)}=F_(lcell)/g (or a filtered version of this), the mass would have tobe still with a right cable for the estimation to be accurate, which isnot useful in practice. The mass is then found with a filtered version{circumflex over (m)}=F_(lcell)/â_(pf). (or an identification technique)where â_(pf) is the fusion method estimation, as provided above.

The human force estimation is used in a float mode at 102 in FIGS. 9 and10. Prior to entering this float mode 102, the payload mass isdetermined at 103, as was explained in the previous section. The humanforce is deduced at 105 from the following equation:

{circumflex over (f)} _(H) =F _(lcell) −{circumflex over (m)} ₀â_(pf)

where â_(pf) is the payload acceleration estimation, as described aboveand the fusion method, F_(lcell) is the load cell 96 signal and{circumflex over (m)}₀ is the payload mass estimation prior to enteringfloat mode. The estimated human force signal can be treated in differentways. First of all, a deadband can be applied to cope with estimationerrors:

$f_{out} = \{ \begin{matrix}0 & {{{if}\mspace{14mu} - F_{dband}} < F_{in} < F_{dband}} \\{f_{in} - f_{dband}} & {{{if}\mspace{14mu} F_{in}} > F_{dband}} \\{f_{in} + f_{dband}} & {{{if}\mspace{14mu} F_{in}} < {- F_{dband}}}\end{matrix} $

Where F_(dband) is a deadband to be defined.

The signal can also be low pass filtered, before and after the deadband.The effect is different and is a design parameter.

The compensation of the dynamical effects and the deadband can also be afunction of each individual dynamical effect. This can be used to reducenoise in the compensation and/or add a deadband for a given dynamicaleffect only if this effect is present. This is useful if the deadbandmust be high, due to high uncertainties.

The absolute signal is slightly filtered to remove high frequency noise.A rate limiter is then applied, which allows the signal to raiserapidly, but to decrease much more slowly to keep the effect a giventime. By way of a non-limiting example, if the signal only passestemporarily to zero, the signal is then converted from zero to one hereheuristically with an exponential function, such as:

1−e^(a) ^(e) ^(w) ^(e)

where w_(e) is the processed signal, and a_(e) is a design parameter.The given dynamical effect deadband and/or compensation is thenmultiplied by this value. For example, if the total uncertainty is 20newtons (N) because four effects each have an uncertainty of 5N, andonly one effect is present, as the cable vertical acceleration, thedeadband could be set to only 5N instead of 20N. The deadband is raisedonly if other effects are present. This must be well tuned so it remainsintuitive to the operator.

Prior to entering the float mode 102, the payload mass is estimated, asdescribed above, and is frozen to this value called {circumflex over(m)}₀. While in the float mode 102, the human force is estimated andprocessed, as also described above. This estimation is sent to anadmittance controller 98 at 107 which computes a command 99 to be sentto the mechanism 22 at 109. The general float mode process is shown inFIG. 9.

Referring now to FIG. 10, a more detailed control scheme is shown. A PIDcontroller is used as the position controller. The payload 12 massestimation could also be used to enhance the control performances.

The admittance controller 98 accepts a force as an input, which ismeasured, and reacts with a displacement, i.e., position or velocity, inthe vertical direction at output at 104. This displacement output, i.e.,position, velocity, and acceleration, are processed to saturation andlimits at 106 and the output displacements, i.e., position, velocity,and acceleration, are sent to the position controller at 110. Thetrajectory to be followed by the mechanism 22 can be prescribed as adesired trajectory. Position control is used since dynamical effects,such as gravity, are permanently acting on the load.

Referring again to FIG. 10, a control scheme is shown at 108. A PIDcontroller is used as the position controller at 110. The payload 12mass estimation could also be used to enhance the control performances.

While the best modes for carrying out the disclosure have been describedin detail, those familiar with the art to which this disclosure relateswill recognize various alternative designs and embodiments forpracticing the disclosure within the scope of the appended claims.

1. A movement system configured for moving a payload, the movementsystem comprising: a bridge crane configured for movement along an Xaxis; a trolley movably attached to the bridge crane and configured formovement along a Y axis, in perpendicular relationship to the X axis; amovement device depending from the trolley, wherein the movement deviceincludes: an attachment portion; a plurality of housings operativelyextending from the attachment portion; a first curved element and asecond curved element extending between respective ends; wherein theends of the first and second curved elements are pivotally attached to arespective one of the plurality of housings; wherein each of the firstand second curved elements forms a partial circle; wherein the firstcurved element defines a first slot and the second curved elementdefines a second slot; wherein the first curved element perpendicularlyoverlaps with the second curved element such that the first slot of thefirst curved element is in perpendicular relationship to the second slotof the second curved element; wherein the first curved element isconfigured to pivot about a first axis and the second curved element isconfigured to pivot about a second axis, which extends in perpendicularrelationship to the first axis; a cable extending from the attachmentportion and through each of the first slot and the second slot; whereinthe cable is configured to pivot relative to the attachment portion suchthat the cable angularly displaces at least one of the first and secondcurved elements about the respective first and second axis; and a cableangle sensor configured to measure the angular displacement of the atleast one of the first and second curved elements.
 2. A movement system,as set forth in claim 1, wherein the movement device further includes acart operatively connected to at least one of the trolley and the bridgecrane; wherein the cart is configured to move along at least one of therespective X axis and Y axis corresponding to angular displacement ofthe at least one of the first and second curved elements.
 3. A movementsystem, as set forth in claim 2, further comprising a controlleroperatively connected between the sensor and the cart; wherein thecontroller is configured to receive a signal from the sensor indicatingthe measure of the angular displacement of the at least one of the firstand second elements and, in turn, send a signal to the cart to move thecart along the at least one of the X axis and the Y axis in response tothe signal received from the sensor.
 4. A movement system, as set forthin claim 3, wherein the movement device further includes: a plurality ofbearings, wherein one of the plurality of bearings is disposed in arespective one of each of the housings; and a plurality of shafts,wherein one of the plurality of shafts pivotally interconnects one ofthe ends of a respective one of the first and second curved elementswith the respective housing such that the shafts are pivotally supportedby the respective bearing.
 5. A movement system, as set forth in claim4, wherein the cable angle sensor includes: a pair of encodersoperatively connected to a respective one of the first curved elementand the second curved element; and a pair of sensors operativelyconnected to a respective one of the first curved element and the secondcurved element; wherein the sensor and the encoder corresponding to therespective first curved element and the second curved element areconfigured to provide a signal to the controller corresponding to theangular displacement of the respective first curved element and secondcurved element.
 6. A movement system, as set forth in claim 5, whereinthe sensors are Hall effect sensors.
 7. A movement system, as set forthin claim 1, the movement device further including a winch configured tomove the cable in a Z direction to vary a length of the cable and movethe payload in the Z direction.
 8. A movement system, as set forth inclaim 7, the movement device further including a load cell operativelyconnected to the cable and configured to sense a load applied to thepayload.
 9. A movement device configured determine a direction ofintended movement of a payload, the movement device comprising: anattachment portion; a plurality of housings operatively extending fromthe attachment portion; a first curved element and a second curvedelement extending between respective ends; wherein the ends of the firstand second curved elements are pivotally attached to a respective one ofthe plurality of housings; wherein each of the first and second curvedelements forms a partial circle; wherein the first curved elementdefines a first slot and the second curved element defines a secondslot; wherein the first curved element perpendicularly overlaps with thesecond curved element such that the first slot of the first curvedelement is in perpendicular relationship to the second slot of thesecond curved element; wherein the first curved element is configured topivot about a first axis and the second curved element is configured topivot about a second axis, which extends in perpendicular relationshipto the first axis; a cable extending from the attachment portion andthrough each of the first slot and the second slot; wherein the cable isconfigured to pivot relative to the attachment portion such that thecable angularly displaces at least one of the first and second curvedelements about the respective first and second axis; and a cable anglesensor configured to measure the angular displacement of the at leastone of the first and second curved elements.
 10. A movement device, asset forth in claim 9, wherein the movement device further includes acart operatively connected to at least one of the trolley and the bridgecrane; wherein the cart is configured to move along at least one of therespective X axis and Y axis corresponding to angular displacement ofthe at least one of the first and second curved elements.
 11. A movementdevice, as set forth in claim 10, further comprising a controlleroperatively connected between the sensor and the cart; wherein thecontroller is configured to receive a signal from the sensor indicatingthe measure of the angular displacement of the at least one of the firstand second elements and, in turn, send a signal to the cart to move thecart along the at least one of the X axis and the Y axis in response tothe signal received from the sensor.
 12. A movement device, as set forthin claim 11, wherein the movement device further includes: a pluralityof bearings, wherein one of the plurality of bearings is disposed in arespective one of each of the housings; and a plurality of shafts,wherein one of the plurality of shafts pivotally interconnects one ofthe ends of a respective one of the first and second curved elementswith the respective housing such that the shafts are pivotally supportedby the respective bearing.
 13. A movement device, as set forth in claim12, wherein the cable angle sensor includes: a pair of encodersoperatively connected to a respective one of the first curved elementand the second curved element; and a pair of sensors operativelyconnected to a respective one of the first curved element and the secondcurved element; wherein the sensor and the encoder corresponding to therespective first curved element and the second curved element areconfigured to provide a signal to the controller corresponding to theangular displacement of the respective first curved element and secondcurved element.
 14. A movement device, as set forth in claim 13, whereinthe sensors are Hall effect sensors.
 15. A movement system, as set forthin claim 9, the movement device further including a winch configured tomove the cable in a Z direction to vary a length of the cable and movethe payload in the Z direction.
 16. A movement system, as set forth inclaim 15, the movement device further including a load cell operativelyconnected to the cable and configured to sense a load applied to thepayload.
 17. A method of moving a movement device along at least one ofan X axis and a Y axis, the method comprising: providing a cable anglesensor configured to measure angular displacement of at least one of afirst and a second curved element about a respective first and secondaxis; disposing a cable vertically through each of a first and secondslot defined in the respective first and second curved element;imparting an angle to the cable such that the cable causes an angulardisplacement of at least one of the first and second curved elementsabout the respective first and second axis; determining the angulardisplacement of the at least one of the first and second curved elementsabout the respective first and second axis; and moving the movementdevice along the at least one of the X axis and the Y axis in responseto the determination of the angular displacement of the at least one ofthe first and second curved elements about the respective first andsecond axis until the cable is vertical.
 18. A method of moving amovement device, as set forth in claim 17, further comprising ceasingmovement of the device along the at least one of the X axis and the Yaxis in response to the determination of the angular displacement the atleast one of the first and second curved element to be zero.
 19. Amethod of moving a movement device, as set forth in claim 17, whereindetermining the angular displacement is further defined as: sensing,with the cable angle sensor, the angular displacement of the at leastone of the first and second curved elements about the respective firstand second axis; calculating, in a controller, a direction of movementalong at least one of the X axis and the Y axis based on the sensedangular displacement of the at least one of the first and second curvedelement about the respective first and second axis; and providing asignal to a cart to move the movement device along the at least one ofthe X axis and the Y axis in response to the calculation of thedirection of movement such that the cable is vertical.
 20. A method ofmoving a movement device, as set forth in claim 19, wherein sensing,with the cable angle sensor, is further defined as sensing, with asensor and an encoder, the angular displacement of the at least one ofthe first and second curved elements; and wherein calculating, in acontroller, is further defined as combining the angular displacementsensed by each of the sensor and the encoder to determine a direction ofmovement along at least one of the X axis and the Y axis.